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The Exact Computation Paradigm
, 1994
"... We describe a paradigm for numerical computing, based on exact computation. This emerging paradigm has many advantages compared to the standard paradigm which is based on fixedprecision. We first survey the literature on multiprecision number packages, a prerequisite for exact computation. Next ..."
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Cited by 94 (10 self)
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We describe a paradigm for numerical computing, based on exact computation. This emerging paradigm has many advantages compared to the standard paradigm which is based on fixedprecision. We first survey the literature on multiprecision number packages, a prerequisite for exact computation. Next we survey some recent applications of this paradigm. Finally, we outline some basic theory and techniques in this paradigm. 1 This paper will appear as a chapter in the 2nd edition of Computing in Euclidean Geometry, edited by D.Z. Du and F.K. Hwang, published by World Scientific Press, 1994. 1 1 Two Numerical Computing Paradigms Computation has always been intimately associated with numbers: computability theory was early on formulated as a theory of computable numbers, the first computers have been number crunchers and the original massproduced computers were pocket calculators. Although one's first exposure to computers today is likely to be some nonnumerical application, numeri...
Computing Roadmaps of General SemiAlgebraic Sets
, 1993
"... In this paper we study the problem of determining whether two points lie in the same connected component of a semialgebraic set S. Although we are mostly concerned with sets S # , our algorithm can also decide if points in an arbitrary set S # R can be joined by a semialgebraic path, for any real ..."
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Cited by 50 (2 self)
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In this paper we study the problem of determining whether two points lie in the same connected component of a semialgebraic set S. Although we are mostly concerned with sets S # , our algorithm can also decide if points in an arbitrary set S # R can be joined by a semialgebraic path, for any real closed field R. Our algorithm computes a onedimensional semialgebraic subset ##S# of S (actually of an embedding of S in a space R for a certain real extension field R of the given field R#. ##S# is called the roadmap of S. The basis of this work is the roadmap algorithm described in [3], [4] whichworked only for compact, regularly stratified sets. We measure...
Topological Queries in Spatial Databases
 Journal of Computer and System Sciences
, 1996
"... We study topological queries over twodimensional spatial databases. First, we show that the topological properties of semialgebraic spatial regions can be completely specified using a classical finite structure, essentially the embedded planar graph of the region boundaries. This provides an invar ..."
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Cited by 44 (2 self)
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We study topological queries over twodimensional spatial databases. First, we show that the topological properties of semialgebraic spatial regions can be completely specified using a classical finite structure, essentially the embedded planar graph of the region boundaries. This provides an invariant characterizing semialgebraic regions up to homeomorphism. All topological queries on semialgebraic regions can be answered by queries on the invariant whose complexity is polynomially related to the original. Also, we show that for the purpose of answering topological queries, semialgebraic regions can always be represented simply as polygonal regions. We then study query languages for topological properties of twodimensional spatial databases, starting from the topological relationships between pairs of planar regions introduced by Egenhofer. We show that the closure of these relationships under appropriate logical operators yields languages which are complete for topological prope...
Automatic construction of simple artifactbased workflows
 In: Proc. of the 12th Int. Conf. on Database Theory (ICDT 2009
, 2009
"... Almost all medium and largescale businesses rely on electronic workflow systems to manage their business processes. A key challenge is to enable the easy reuse and modification of these workflow schemas and their pieceparts, so that they can be adapted to new business situations. This paper desc ..."
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Cited by 22 (2 self)
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Almost all medium and largescale businesses rely on electronic workflow systems to manage their business processes. A key challenge is to enable the easy reuse and modification of these workflow schemas and their pieceparts, so that they can be adapted to new business situations. This paper describes an approach for automatic construction (and thus, evolution) of a workflow schema that satisfies a specified condition (or “goal”), starting from a set of basic building block services (or “tasks”). We use a workflow model based on “business artifacts”, which represent key (real or conceptual) business entities, and include both the businessrelevant data about them and a specification of their lifecycle, that is, how they can evolve over time as they move through the workflow as the result of services being applied to them. This paper uses a declarative form of artifactcentric workflow. The
Querying Spatial Databases via Topological Invariants
 In PODS'98
, 1998
"... The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases. The focus is on the translation of topological queries against the spatial database into queries against the topological invariant. The languages considered ..."
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Cited by 16 (2 self)
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The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases. The focus is on the translation of topological queries against the spatial database into queries against the topological invariant. The languages considered are firstorder on the spatial database side, and fixpoint + counting, fixpoint, and firstorder on the topological invariant side. In particular, it is shown that fixpoint + counting expresses precisely all the ptime queries on topological invariants; if the regions are connected, fixpoint expresses all ptime queries on topological invariants. 1 Introduction Spatial data is an increasingly important part of database systems. It is present in a wide range of applications: geographic information systems, video databases, medical imaging, CADCAM, VLSI, robotics, etc. Different applications pose different requirements on query languages and therefore on the kind of spatial information th...
Computation of Equilibria in Noncooperative Games
 IN PROC. WORKSHOP FOR COMPUTABLE ECONOMICS
, 2000
"... This paper presents algorithms for finding equilibria of mixed strategy in multistage noncooperative games of incomplete information (like probabilistic blindfold chess, where at every opportunity a player can perform different moves with some probability). These algorithms accept input games in ..."
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Cited by 9 (4 self)
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This paper presents algorithms for finding equilibria of mixed strategy in multistage noncooperative games of incomplete information (like probabilistic blindfold chess, where at every opportunity a player can perform different moves with some probability). These algorithms accept input games in extensive form. Our main result is an algorithm for computing Sequential equilibrium, which is the most widely accepted notion of equilibrium (for mixed strategies of noncooperative probabilistic games) in mainstream economic game theory. Previously, there were no known algorithms for computing sequential equilibria strategies (except for the special case of single stage games). The computational aspects of passage from a recursive presentation of a game to its extensive form are also discussed. For nontrivial inputs the concatenation of this procedure with the equilibrium computation is time intensive, but has low spatial requirements. Given a recursively represented game, with a po...
Computing the Newtonian Graph
, 1997
"... Introduction Following Smale (1985), we define the Newtonian vector field of a polynomial f 2 C [z] by N f (z) = \Gammaf (z)=f 0 (z). The name is derived from Newton's method for root approximation, in which successive approximations to a root of f are computed by the rule x k+1 / x k +N f (x k ..."
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Cited by 3 (0 self)
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Introduction Following Smale (1985), we define the Newtonian vector field of a polynomial f 2 C [z] by N f (z) = \Gammaf (z)=f 0 (z). The name is derived from Newton's method for root approximation, in which successive approximations to a root of f are computed by the rule x k+1 / x k +N f (x k ). The vector field N f defines a flow on C , where the flow comes almost everywhere from a pole (in the affine case where f is a polynomial, from 1) and converges almost everywhere to a root of f . Each discrete step in Newton's method is tangent to a curve of flow. We can think of a curve of flow as the trajectory a particle would take under a v
Exploration of Geographic Databases: Supporting a Focus+Context Interaction Style
 Journal of Applied System Studies
, 2001
"... Introduction Geographic Information Systems (GISs) deal with storing, querying, manipulating and displaying geographic information. The core of a GIS is a spatial database management system handling the spatial and the thematic components of the database. The spatial component encodes the geometric ..."
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Cited by 1 (1 self)
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Introduction Geographic Information Systems (GISs) deal with storing, querying, manipulating and displaying geographic information. The core of a GIS is a spatial database management system handling the spatial and the thematic components of the database. The spatial component encodes the geometric aspects of the physical objects under consideration (location, shape, orientation, and size), while the thematic component contains information about the nongeometric properties of the realm of interest. A GIS normally includes modules devoted to application specific tasks, such as map production, spatial analysis, and data visualisation. We are interested here in studying some aspects related to the visualisation of and the interaction with geographic maps, with focus on navigational tasks (following [Nigay (1998)], an interaction task is said navigational when the user is directly responsible for it). Navigational paradigms are acquiring growing relevance with the advent of webbased ap
Lower Bounds for Shortest Path and Related Problems
 In Proc. 28th Ann. IEEE
, 1987
"... We present the first lower bounds for shortest path problems (including euclidean shortest path) in three dimensions, and for some constrained motion planning problems in two and three dimensions. Our proofs are based a technique called free path encoding and use homotopy equivalence classes of ..."
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Cited by 1 (0 self)
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We present the first lower bounds for shortest path problems (including euclidean shortest path) in three dimensions, and for some constrained motion planning problems in two and three dimensions. Our proofs are based a technique called free path encoding and use homotopy equivalence classes of paths to encode state. We first apply the method to the shortest path problem in three dimensions. The problem is to find the shortest path under an L p metric (e.g. a euclidean metric) between two points amid polyhedral obstacles. Although this problem has been extensively studied, there were no previously known lower bounds. We show that there may be exponentially many shortest path classes in singlesource multipledestination problems, and that the singlesource singledestination problem is NPhard. We use a similar proof technique to show that two dimensional dynamic motion planning with bounded velocity is NPhard. Finally we extend the technique to compliant motion planni...